Contents. Bibliografische Informationen digitalisiert durch

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1 Part I Methodology 1 Introduction Basic Concepts Preliminary Examples Vanilla Interest-Rate Swap Cancellable Swap Managing Credit Risk Collateral, Credit Default Swap Why Compute Counterparty Credit Exposure? Modelling Counterparty Credit Exposure Definition Risk Measures Netting and Aggregation Close-OutRisk Right-Way/Wrong-Way Exposure Credit Valuation Adjustment: CVA A Simple Credit Quantification Example Computing Credit Exposure by Simulation Implementation Challenges An Alternative Approach: The AMC Algorithm Which Architecture? WhatNext? 21 2 Modelling Framework Counterparty Credit Exposure Definition Process Dynamics Interest Rate: Single Currency Simple Specifications HJM Framework Libor Market Models Multiple Currencies and Foreign Exchange Inflation xv Bibliografische Informationen digitalisiert durch

2 xvi Contents 2.6 Equity Credit Default Probabilities from par CDS Spreads Stochastic Default Probabilities Loss Simulation 42 3 Simulation Models Interest-Rate Models Separable Volatility Example: Hull-White (Extended Vasicek) Equity and FX Models BlackModel Local Volatility Stochastic Volatility Jump Models Extension to Stochastic Interest Rates A Simpler Approach: Independent Interest Rates Different Models for Different Markets CreditModels Simulation of Single-Name Default Probabilities and Default Times Inter-Name Default Dependence Technical Note: Recursion Properties of the Loss Distribution: Large Homogeneous Portfolio Calibration of Correlation Choice of Model 75 4 Valuation and Sensitivities American Monte Carlo: Mathematical Notation and Description Mathematical Formulation Practical Examples Backward Induction Algorithm AMC Estimation Algorithms Tilley's Algorithm Longstaff-Schwartz Regression Biases of Estimates An AMC Algorithm to Compute Credit Exposure Post-Processing of the Price Distribution Practical Examples Revisited Computing Price Sensitivities The Classical Approach Price Sensitivities through Regression Removing Correlation Extensions

3 xvü Part П Architecture and Implementation 5 Computational Framework AMC Implementation and Trade Representation Examples Expression Trees A Portfolio Aggregation Language PAL Examples The Concept of Scenarios The Concept of Super-Product An Example of Super-Products: The C-CDS Implementation Ill 6.1 Spot and Forward Statistics Ill Libor Rates and Bond Prices Annuity Swap Rate Path Dependent Statistics Extremum Average In Range Fraction CreditLoss Monte Carlo Stepping Technical Notes SDE Integration Schemes Milstein 2 Scheme Martingale Interpolation Distribution of Maxima and Minima Error Analysis Choice of Model: Scenario and Exposure Analysis AMC Error Numerical Errors Approximations: Arbitrage Conditions Architecture Requirements Functional, Non-Functional Requirements, and Design Principles Conceptual View: Methodology Logical View Portfolio Manager Components State of the World Components Quantification Components Physical View Alternative Approaches 144

4 Part HI Products 8 Interest-Rate Products Interest-Rate Swaps Swaps in Advance and in Arrears Capped and Floored Swaps Cancellable Swaps Cross-Currency Swaps Constant-Maturity Swaps and Steepeners Range Accruals Interest-Rate Options Equity, Commodity, Inflation and FX Products Forwards and Options Forwards Contracts Vanilla and Digital Options Bermudan and American Options Asian Options Barrier Options Asset Swaps Absolute Return Swaps Relative Return Swaps Cliquets Target Redemption Swaps Credit Derivatives Credit Default Swaps Collateral Debt Obligations Structures Sinking Funds Accelerated Share Re-Purchase Callable Daily Accrual Notes Call Spread Overlays 179 Part IV Hedging and Managing Counterparty Risk 12 Counterparty Risk Aggregation and Risk Mitigation Risk Measures Choice of Measure Portfolio Risk Aggregation Reference Currency Netting and No-Netting Agreements BreakClauses Collateral Agreements Counterparty Exposure of Collateralised Counterparties.. 191

5 xix Examples Close-Out Risk Risk Allocation Naive Allocation Euler Allocation Comparison with Naive Allocation Contribution Calculation of Collateralised Transactions Combining Market and Credit Risk Change of Measure: Practical Implementation Exposure under Real-World Measure Stress Testing Right-Way /Wrong-Way Exposure Right-Way/Wrong-Way Exposure: Merton Approach The Inverse Problem Example 1: Call Option on Stock Example 2: Call Put Structure on Oil Example 3: Cross-Currency Swap on USD-GBP Comparison with the Change of Measure Approach Pricing Counterparty Credit Risk Credit Valuation Adjustment and Static Hedging Contingent Credit Default Swap American Monte Carlo Valuation Example Dynamic Hedging of Counterparty Risk Optimal Static Hedging CVA Sensitivities Collateral Agreements Right-Way/Wrong-Way Risk Examples С-CDS on a Vanilla Interest-Rate Swap Impact of Discretization Schedule Collateralised Equity Swap Case Study 226 Concluding Remarks 231 A Approximations 233 A.I Maximum Likely Exposure 233 A.1.1 MLE of Equity and FX Products 233 A.1.2 MLE of Swaps 234 A.2 Expected Positive Exposure 235 A.2.1 EPE and CVA of Equity Options 235 A.2.2 Relation between MLE, EPE 235 A.3 CVA of Swaps 236

6 xx Contents В Results from Stochastic Calculus and Finance B.I Brownian Motion and Martingales 239 B.2 Replication of Contingent Claims: Martingale Representation B.3 Change of Numeraire 243 References 245 Index 249